This is a category D study. The development of mucous stasis within the lungs of patients with cystic fibrosis leads to airway obstruction. When combined with deficient mechanisms for clearing bacteria, a microenvironment is created, conducive to infection. The presence of bacteria provides a chronic immunologic stimulus to the patient's host defense system. This leads to the recruitment and activation of large numbers of white blood cells into the airspaces of the lung. These cells then release massive quantities of toxic substances, which serve to further propagate the inflammatory response and directly mediate lung damage. The most important white blood cell-derived substance toxic to the lung is human neutrophil elastase. This study is designed to assess the ability of a neutrophil elastase inhibitor, DMP 777, administered by mouth several times daily to patients with cystic fibrosis. Inhibition of human neutrophil elastase will be measured in bronchoalveolar lavage fluids obtained fourteen days after treatment has started.